In the number series 3, 7, 13, 27, 53, 107, the next term is _______. – UGC NET Question

The pattern alternates between multiplying by 2 and adding 1, and multiplying by 2 and subtracting 1. Specifically, 3 × 2 + 1 = 7, 7 × 2 − 1 = 13, 13 × 2 + 1 = 27, 27 × 2 − 1 = 53 and 53 × 2 + 1 = 107. The next step should follow the "×2 − 1" rule. Thus, 107 × 2 − 1 = 214 − 1 = 213, which fits the alternating structure.

Option A:
Option A gives 211, which would correspond to subtracting 3 after doubling and does not follow the precise "minus one" part of the pattern. This breaks the carefully balanced alternation between adding and subtracting 1. Therefore, 211 is not consistent with the rule.

Option B:
Option B yields 213, which is obtained by 107 × 2 − 1 and continues the alternating pattern exactly. The series 3, 7, 13, 27, 53, 107, 213 remains governed by a single, well-defined recursive rule. Hence, 213 is the correct next term.

Option C:
Option C suggests 215, which would require adding 1 after doubling instead of subtracting 1 at this step. That would repeat the previous type of operation and disrupt the alternation. Thus, 215 is not the appropriate continuation.

Option D:
Option D offers 217, which is even further away and would demand a completely different adjustment after doubling. This option ignores the subtle alternation at the heart of the sequence. Therefore, 217 cannot be accepted as correct.